Intermittent Demand: Spare Parts

Every method in this chapter is judged twice: once on how close its forecast came, and once on whether the stock it implied served the customer. The two answers do not agree, and the gap between them is the chapter.

The extract arrived with 9,420 rows for what should be 60 parts across 156 weeks. One week had been extracted twice, one part number was written three ways, a customer return was booked as minus eleven units and a stock count of 9,999 had been typed into the issues column. After cleaning, 60 parts, 156 weeks and 17,925 units issued in total.

The classification is the Syntetos-Boylan-Croston scheme: how many weeks pass between orders, and how much the order sizes vary. Both cut-offs are the published ones. Here it gives 26 lumpy, 21 intermittent, 7 erratic and 6 smooth, and the four groups need different things, which is the reason for classifying at all.

A part that has stopped moving and a part that moves rarely look identical in a spreadsheet, and they need opposite decisions. The way to tell them apart is to measure silence in units of that part's own rhythm rather than in weeks.

Fourteen times its own gap, against a runner-up at four. P1024 was superseded by a newer part number partway through the history. In the year that was held back it was issued zero units, and every method in this chapter would have produced a small positive forecast for it, the warehouse would have stocked it, and the stock would never have moved.

Four weeks of quiet means nothing for a part ordered twice a year and a great deal for one ordered every fortnight. That is why the test is a ratio. It is a decision about the catalog rather than about forecasting, and it belongs before any of it: P1024 is excluded, leaving 59 parts.

The planning tool reports a mean absolute percentage error every month. A percentage error divides by the actual demand. On a week when nothing was demanded, there is nothing to divide by.

Those are the easy weeks. A forecast is roughly right about a week with demand far more often than it is right about which weeks will have any, so the measure was scoring the part of the problem that was not the problem. It did not fail loudly. It dropped the undefined rows and averaged what was left.

The replacement used from here is MASE, the mean absolute scaled error, which divides by the average absolute week-to-week change of the series itself rather than by the actual. It is defined on zeros, it is comparable across parts of very different sizes, and below 1 means the forecast beat a rule that just repeats last week.

Two years of history for each part, one number out. Croston's method is the one built for this problem: instead of smoothing the raw series, it smooths the order size and the interval between orders separately and divides one by the other. SBA is Croston with the Syntetos-Boylan correction, a multiplier of one minus half the smoothing constant, which exists because a ratio of two smoothed estimates is biased upward.

SBA is best overall, and the margin over plain exponential smoothing is 0.002. It wins the erratic and lumpy classes, where sizes swing about and the upward bias bites hardest, and it loses the intermittent class to the naive rule. The Syntetos-Boylan correction is worth 0.014 MASE against uncorrected Croston, which is small and free.

The naive rule is the worst overall by a wide margin, and it is worth pausing on why that is not obvious: on the aggregate warehouse series in the first picture, repeating last week would have looked perfectly respectable.

Three of the four methods land within two percent of one another. That is not because the methods resemble each other. It is a property of the measure, and the cleanest way to see it is to ask what the best possible constant forecast would have been, chosen with hindsight.

Mean absolute error is minimized at the median, and for a part ordered once a month the median week contains no demand at all. So a scoreboard built on absolute error rewards whichever method leans lowest, and the outright winner of that contest is a policy that never orders anything. It beats all four honest methods by a wide margin.

This is the metric lesson from Chapter 198 in its most extreme form. The measure has to come from the decision. The decision here is how many units to hold, and that is answered by a quantile of demand over the lead time. It is not answered by an average of weekly demand, and it is certainly not answered by whichever method minimizes an error statistic.

A forecast of 0.74 units a week is never the demand in any week. The warehouse orders against a level: hold this many, top up weekly, and the supplier takes two weeks. So the quantity to get right is total demand over the three weeks an order has to cover, and specifically a high quantile of it.

Ordering to the middle fills fewer than one unit in ten. That is not a broken calculation. Half of all three-week windows fall above the middle, and in demand shaped like this the ones that do fall a long way above. Everything past the middle is safety stock, and how much of it to hold is the decision the warehouse is really making.

Every live part run through the policy, for each method and each service quantile, scored on the year that was held back.

At the service level the business asked for, the four methods span 3.0 points of fill rate, and most of that is the naive rule being poor. Holding the method fixed and moving the quantile moves the fill rate by 52.1 points. The choice nobody discusses has seventeen times the leverage of the choice everyone argues about.

That is not an argument for choosing a method carelessly. SBA is free and slightly better, so use it. It is an argument about where the attention belongs, and in most warehouses it is pointed at the forecast.

Asking for the 0.95 quantile of lead-time demand delivered a fill rate of 92.7 percent, not 95. Those are different quantities. The quantile controls how often a replenishment cycle runs short; the fill rate counts units, and a cycle that runs short by twenty units counts worse than one that runs short by one. If the business has agreed a fill rate, the quantile has to be tuned until the simulation delivers it.

The last few points of service cost twenty-seven times what the first ones did. Going from 44 to 87 percent costs six units a part. The next nine points cost twelve more. That curve, and not the forecast, is what a service-level conversation should be held over, because it is the only place in this chapter where the business is being asked to spend money.

One smoothing constant, never tuned. Every method here uses 0.10, the conventional default for intermittent demand. Tuning it per part on a rolling origin would tighten the forecasts a little and would not move the service curve, which is the part that matters.

The spread came from history, not from a model. The order-up-to level takes its level from the forecast and its spread from that part's own past three-week windows. A part whose pattern is changing gets a stale spread and nothing here would notice.

Fill rate is not the only service measure. Counting units treats one customer waiting for twenty parts the same as twenty customers waiting for one each. If the second is worse for the business, the target should not be a fill rate.

Every part was treated as its own problem. Parts that fail together, or that substitute for one another, break that assumption in opposite directions. For sixty parts that is defensible. For sixty thousand it is where the remaining gains are.

• ✓Count the zeros before choosing an error measure. If a percentage error is being reported on a series with zeros in it, something is being dropped, and it is usually the majority of the data.
• ✓Separate the dead from the slow first. Measure silence in units of the part's own inter-order interval, not in weeks, and set the threshold where the ratio separates cleanly.
• ✓Classify before you compare. The four classes reward different methods, and an average over all of them hides that the naive rule is winning a quarter of your catalog.
• ✓Ask what the error-minimizing forecast would be. If it is zero, the measure is not aligned with the decision and no amount of method selection will fix that.
• ✓Simulate the policy, do not assume the service level. A 0.95 quantile is not a 95 percent fill rate, and the only way to know the gap is to run the year through the policy.
• ✓Put the service curve in front of whoever sets the target. The last few points of fill rate cost several times what the first ones did, and that is a business decision rather than a forecasting one.

Intermittency is the standard case in service parts, and it appears wherever events are rare enough that most periods are empty. In all of them the useful output is a distribution rather than a number, and most forecasting stacks return a number.